This paper deals with the existence of positive solutions to the following nonlinear Kirchhoff equation with perturbed external source terms: $$ \left\{ \begin{array}{ll} -\Big(a+b \int_{\mathbb{R}^3} | \nabla u |^2 {\rm d}x\Big) \Delta u+ V(x)u=Q(x)u^p+\varepsilon f(x),\quad &x\in \mathbb{R}^3, \\ u>0,\quad &u\in H^1(\mathbb{R}^3). \end{array} \right.$$ Here $a,b$ are positive constants, $V(x),Q(x)$ are positive radial potentials, 1<p<5, $\varepsilon$ >0 is a small parameter, $f(x)$ is an external source term in $L^2(\mathbb{R}^3)\cap L^{\infty}(\mathbb{R}^3)$.
Narimane AISSAOUI
,
Wei LONG
. POSITIVE SOLUTIONS FOR A KIRCHHOFF EQUATION WITH PERTURBED SOURCE TERMS[J]. Acta mathematica scientia, Series B, 2022
, 42(5)
: 1817
-1830
.
DOI: 10.1007/s10473-022-0507-z
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